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489 lines
16 KiB
Java
489 lines
16 KiB
Java
/*
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* Copyright 2009 Google Inc.
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may not
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* use this file except in compliance with the License. You may obtain a copy of
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* the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations under
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* the License.
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*/
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with this
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* work for additional information regarding copyright ownership. The ASF
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* licenses this file to You under the Apache License, Version 2.0 (the
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* "License"); you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations under
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* the License.
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*
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* INCLUDES MODIFICATIONS BY RICHARD ZSCHECH AS WELL AS GOOGLE.
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*/
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package java.math;
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/**
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* Static library that provides {@link BigInteger} base conversion from/to any
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* integer represented in a {@link java.lang.String} Object.
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*/
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class Conversion {
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/**
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* bigRadices values are precomputed maximal powers of radices (integer
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* numbers from 2 to 36) that fit into unsigned int (32 bits). bigRadices[0] =
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* 2 ^ 31, bigRadices[8] = 10 ^ 9, etc.
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*/
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static final int bigRadices[] = {
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-2147483648, 1162261467, 1073741824, 1220703125, 362797056, 1977326743,
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1073741824, 387420489, 1000000000, 214358881, 429981696, 815730721,
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1475789056, 170859375, 268435456, 410338673, 612220032, 893871739,
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1280000000, 1801088541, 113379904, 148035889, 191102976, 244140625,
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308915776, 387420489, 481890304, 594823321, 729000000, 887503681,
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1073741824, 1291467969, 1544804416, 1838265625, 60466176};
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/**
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* Holds the maximal exponent for each radix, so that
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* radix<sup>digitFitInInt[radix]</sup> fit in an {@code int} (32 bits).
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*/
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static final int[] digitFitInInt = {
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-1, -1, 31, 19, 15, 13, 11, 11, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7,
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7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5};
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/**
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* @see BigInteger#toString(int)
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* @param val
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* @param radix
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* @return
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*/
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static String bigInteger2String(BigInteger val, int radix) {
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int sign = val.sign;
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int numberLength = val.numberLength;
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int digits[] = val.digits;
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if (sign == 0) {
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return "0"; //$NON-NLS-1$
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}
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if (numberLength == 1) {
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int highDigit = digits[numberLength - 1];
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long v = highDigit & 0xFFFFFFFFL;
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if (sign < 0) {
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v = -v;
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}
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return Long.toString(v, radix);
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}
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if ((radix == 10) || (radix < Character.MIN_RADIX)
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|| (radix > Character.MAX_RADIX)) {
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return val.toString();
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}
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double bitsForRadixDigit;
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bitsForRadixDigit = Math.log(radix) / Math.log(2);
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int resLengthInChars = (int) (val.abs().bitLength() / bitsForRadixDigit + ((sign < 0)
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? 1 : 0)) + 1;
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char result[] = new char[resLengthInChars];
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int currentChar = resLengthInChars;
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int resDigit;
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if (radix != 16) {
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int temp[] = new int[numberLength];
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System.arraycopy(digits, 0, temp, 0, numberLength);
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int tempLen = numberLength;
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int charsPerInt = digitFitInInt[radix];
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int i;
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// get the maximal power of radix that fits in int
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int bigRadix = bigRadices[radix - 2];
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while (true) {
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// divide the array of digits by bigRadix and convert remainders
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// to characters collecting them in the char array
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resDigit = Division.divideArrayByInt(temp, temp, tempLen, bigRadix);
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int previous = currentChar;
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do {
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result[--currentChar] = Character.forDigit(resDigit % radix, radix);
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} while (((resDigit /= radix) != 0) && (currentChar != 0));
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int delta = charsPerInt - previous + currentChar;
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for (i = 0; i < delta && currentChar > 0; i++) {
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result[--currentChar] = '0';
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}
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for (i = tempLen - 1; (i > 0) && (temp[i] == 0); i--) {
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// empty
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}
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tempLen = i + 1;
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if ((tempLen == 1) && (temp[0] == 0)) { // the quotient is 0
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break;
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}
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}
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} else {
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// radix == 16
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for (int i = 0; i < numberLength; i++) {
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for (int j = 0; (j < 8) && (currentChar > 0); j++) {
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resDigit = digits[i] >> (j << 2) & 0xf;
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result[--currentChar] = Character.forDigit(resDigit, 16);
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}
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}
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}
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while (result[currentChar] == '0') {
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currentChar++;
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}
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if (sign == -1) {
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result[--currentChar] = '-';
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}
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return new String(result, currentChar, resLengthInChars - currentChar);
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}
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static long divideLongByBillion(long a) {
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long quot;
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long rem;
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if (a >= 0) {
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long bLong = 1000000000L;
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quot = (a / bLong);
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rem = (a % bLong);
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} else {
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/*
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* Make the dividend positive shifting it right by 1 bit then get the
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* quotient an remainder and correct them properly
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*/
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long aPos = a >>> 1;
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long bPos = 1000000000L >>> 1;
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quot = aPos / bPos;
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rem = aPos % bPos;
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// double the remainder and add 1 if 'a' is odd
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rem = (rem << 1) + (a & 1);
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}
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return ((rem << 32) | (quot & 0xFFFFFFFFL));
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}
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/**
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* Builds the correspondent {@code String} representation of {@code val} being
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* scaled by {@code scale}.
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*
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* @see BigInteger#toString()
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* @see BigDecimal#toString()
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*/
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static String toDecimalScaledString(BigInteger val, int scale) {
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int sign = val.sign;
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int numberLength = val.numberLength;
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int digits[] = val.digits;
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int resLengthInChars;
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int currentChar;
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char result[];
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if (sign == 0) {
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switch (scale) {
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case 0:
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return "0"; //$NON-NLS-1$
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case 1:
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return "0.0"; //$NON-NLS-1$
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case 2:
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return "0.00"; //$NON-NLS-1$
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case 3:
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return "0.000"; //$NON-NLS-1$
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case 4:
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return "0.0000"; //$NON-NLS-1$
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case 5:
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return "0.00000"; //$NON-NLS-1$
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case 6:
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return "0.000000"; //$NON-NLS-1$
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default:
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StringBuilder result1 = new StringBuilder();
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if (scale < 0) {
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result1.append("0E+"); //$NON-NLS-1$
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} else {
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result1.append("0E"); //$NON-NLS-1$
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}
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result1.append(-scale);
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return result1.toString();
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}
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}
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// one 32-bit unsigned value may contains 10 decimal digits
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resLengthInChars = numberLength * 10 + 1 + 7;
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// Explanation why +1+7:
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// +1 - one char for sign if needed.
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// +7 - For "special case 2" (see below) we have 7 free chars for
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// inserting necessary scaled digits.
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result = new char[resLengthInChars + 1];
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// allocated [resLengthInChars+1] characters.
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// a free latest character may be used for "special case 1" (see
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// below)
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currentChar = resLengthInChars;
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if (numberLength == 1) {
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int highDigit = digits[0];
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if (highDigit < 0) {
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long v = highDigit & 0xFFFFFFFFL;
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do {
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long prev = v;
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v /= 10;
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result[--currentChar] = (char) (0x0030 + ((int) (prev - v * 10)));
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} while (v != 0);
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} else {
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int v = highDigit;
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do {
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int prev = v;
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v /= 10;
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result[--currentChar] = (char) (0x0030 + (prev - v * 10));
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} while (v != 0);
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}
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} else {
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int temp[] = new int[numberLength];
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int tempLen = numberLength;
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System.arraycopy(digits, 0, temp, 0, tempLen);
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BIG_LOOP : while (true) {
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// divide the array of digits by bigRadix and convert
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// remainders
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// to characters collecting them in the char array
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long result11 = 0;
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for (int i1 = tempLen - 1; i1 >= 0; i1--) {
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long temp1 = (result11 << 32) + (temp[i1] & 0xFFFFFFFFL);
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long res = divideLongByBillion(temp1);
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temp[i1] = (int) res;
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result11 = (int) (res >> 32);
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}
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int resDigit = (int) result11;
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int previous = currentChar;
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do {
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result[--currentChar] = (char) (0x0030 + (resDigit % 10));
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} while (((resDigit /= 10) != 0) && (currentChar != 0));
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int delta = 9 - previous + currentChar;
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for (int i = 0; (i < delta) && (currentChar > 0); i++) {
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result[--currentChar] = '0';
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}
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int j = tempLen - 1;
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for (; temp[j] == 0; j--) {
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if (j == 0) { // means temp[0] == 0
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break BIG_LOOP;
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}
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}
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tempLen = j + 1;
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}
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while (result[currentChar] == '0') {
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currentChar++;
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}
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}
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boolean negNumber = (sign < 0);
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int exponent = resLengthInChars - currentChar - scale - 1;
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if (scale == 0) {
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if (negNumber) {
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result[--currentChar] = '-';
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}
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return new String(result, currentChar, resLengthInChars - currentChar);
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}
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if ((scale > 0) && (exponent >= -6)) {
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if (exponent >= 0) {
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// special case 1
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int insertPoint = currentChar + exponent;
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for (int j = resLengthInChars - 1; j >= insertPoint; j--) {
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result[j + 1] = result[j];
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}
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result[++insertPoint] = '.';
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if (negNumber) {
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result[--currentChar] = '-';
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}
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return new String(result, currentChar, resLengthInChars - currentChar
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+ 1);
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}
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// special case 2
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for (int j = 2; j < -exponent + 1; j++) {
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result[--currentChar] = '0';
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}
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result[--currentChar] = '.';
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result[--currentChar] = '0';
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if (negNumber) {
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result[--currentChar] = '-';
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}
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return new String(result, currentChar, resLengthInChars - currentChar);
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}
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int startPoint = currentChar + 1;
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int endPoint = resLengthInChars;
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StringBuilder result1 = new StringBuilder(16 + endPoint - startPoint);
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if (negNumber) {
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result1.append('-');
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}
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if (endPoint - startPoint >= 1) {
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result1.append(result[currentChar]);
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result1.append('.');
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result1.append(result, currentChar + 1, resLengthInChars - currentChar
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- 1);
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} else {
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result1.append(result, currentChar, resLengthInChars - currentChar);
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}
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result1.append('E');
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if (exponent > 0) {
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result1.append('+');
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}
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result1.append(Integer.toString(exponent));
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return result1.toString();
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}
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/* can process only 32-bit numbers */
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static String toDecimalScaledString(long value, int scale) {
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int resLengthInChars;
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int currentChar;
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char result[];
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boolean negNumber = value < 0;
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if (negNumber) {
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value = -value;
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}
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if (value == 0) {
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switch (scale) {
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case 0:
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return "0"; //$NON-NLS-1$
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case 1:
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return "0.0"; //$NON-NLS-1$
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case 2:
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return "0.00"; //$NON-NLS-1$
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case 3:
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return "0.000"; //$NON-NLS-1$
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case 4:
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return "0.0000"; //$NON-NLS-1$
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case 5:
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return "0.00000"; //$NON-NLS-1$
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case 6:
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return "0.000000"; //$NON-NLS-1$
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default:
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StringBuilder result1 = new StringBuilder();
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if (scale < 0) {
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result1.append("0E+"); //$NON-NLS-1$
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} else {
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result1.append("0E"); //$NON-NLS-1$
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}
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result1.append((scale == Integer.MIN_VALUE)
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? "2147483648" : Integer.toString(-scale)); //$NON-NLS-1$
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return result1.toString();
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}
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}
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// one 32-bit unsigned value may contains 10 decimal digits
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resLengthInChars = 18;
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// Explanation why +1+7:
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// +1 - one char for sign if needed.
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// +7 - For "special case 2" (see below) we have 7 free chars for
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// inserting necessary scaled digits.
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result = new char[resLengthInChars + 1];
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// Allocated [resLengthInChars+1] characters.
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// a free latest character may be used for "special case 1" (see below)
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currentChar = resLengthInChars;
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long v = value;
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do {
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long prev = v;
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v /= 10;
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result[--currentChar] = (char) (0x0030 + (prev - v * 10));
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} while (v != 0);
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long exponent = (long) resLengthInChars - (long) currentChar - scale - 1L;
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if (scale == 0) {
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if (negNumber) {
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result[--currentChar] = '-';
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}
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return new String(result, currentChar, resLengthInChars - currentChar);
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}
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if (scale > 0 && exponent >= -6) {
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if (exponent >= 0) {
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// special case 1
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int insertPoint = currentChar + (int) exponent;
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for (int j = resLengthInChars - 1; j >= insertPoint; j--) {
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result[j + 1] = result[j];
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}
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result[++insertPoint] = '.';
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if (negNumber) {
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result[--currentChar] = '-';
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}
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return new String(result, currentChar, resLengthInChars - currentChar
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+ 1);
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}
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// special case 2
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for (int j = 2; j < -exponent + 1; j++) {
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result[--currentChar] = '0';
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}
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result[--currentChar] = '.';
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result[--currentChar] = '0';
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if (negNumber) {
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result[--currentChar] = '-';
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}
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return new String(result, currentChar, resLengthInChars - currentChar);
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}
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int startPoint = currentChar + 1;
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int endPoint = resLengthInChars;
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StringBuilder result1 = new StringBuilder(16 + endPoint - startPoint);
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if (negNumber) {
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result1.append('-');
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}
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if (endPoint - startPoint >= 1) {
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result1.append(result[currentChar]);
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result1.append('.');
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result1.append(result, currentChar + 1, resLengthInChars - currentChar
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- 1);
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} else {
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result1.append(result, currentChar, resLengthInChars - currentChar);
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}
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result1.append('E');
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if (exponent > 0) {
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result1.append('+');
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}
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result1.append(Long.toString(exponent));
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return result1.toString();
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}
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/**
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* Just to denote that this class can't be instantiated.
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*/
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private Conversion() {
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}
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// /**
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// * @see BigInteger#doubleValue()
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// */
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// static double bigInteger2Double(BigInteger val) {
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// // val.bitLength() < 64
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// if ((val.numberLength < 2)
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// || ((val.numberLength == 2) && (val.digits[1] > 0))) {
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// return val.longValue();
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// }
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// // val.bitLength() >= 33 * 32 > 1024
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// if (val.numberLength > 32) {
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// return ((val.sign > 0) ? Double.POSITIVE_INFINITY
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// : Double.NEGATIVE_INFINITY);
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// }
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// int bitLen = val.abs().bitLength();
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// long exponent = bitLen - 1;
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// int delta = bitLen - 54;
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// // We need 54 top bits from this, the 53th bit is always 1 in lVal.
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// long lVal = val.abs().shiftRight(delta).longValue();
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// /*
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// * Take 53 bits from lVal to mantissa. The least significant bit is
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// * needed for rounding.
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// */
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// long mantissa = lVal & 0x1FFFFFFFFFFFFFL;
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// if (exponent == 1023) {
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// if (mantissa == 0X1FFFFFFFFFFFFFL) {
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// return ((val.sign > 0) ? Double.POSITIVE_INFINITY
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// : Double.NEGATIVE_INFINITY);
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// }
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// if (mantissa == 0x1FFFFFFFFFFFFEL) {
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// return ((val.sign > 0) ? Double.MAX_VALUE : -Double.MAX_VALUE);
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// }
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// }
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// // Round the mantissa
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// if (((mantissa & 1) == 1)
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// && (((mantissa & 2) == 2) || BitLevel.nonZeroDroppedBits(delta,
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// val.digits))) {
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// mantissa += 2;
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// }
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// mantissa >>= 1; // drop the rounding bit
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// long resSign = (val.sign < 0) ? 0x8000000000000000L : 0;
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// exponent = ((1023 + exponent) << 52) & 0x7FF0000000000000L;
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// long result = resSign | exponent | mantissa;
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// return Double.longBitsToDouble(result);
|
|
// }
|
|
}
|